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  1. #1
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    integrals #2

    Please help me with these problems. Thank you.
    1. integral from 0 to pi of (4 sin theta -3 cos theta) d theta
    I started like this...4 integral from 0 to pi of sin theta d theta -3 integral from 0 to pi cos theta d theta...I got stuck here
    2. How do I calculate this math?
    3/4 (8^4/3) - 3/4 (1^4/3) =?
    3. How do I solve this integral?
    integral of cos^3 x dx
    Thanks again for your help!
    Last edited by mr fantastic; October 5th 2009 at 04:27 AM. Reason: Re-titled post
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  2. #2
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    1. integral from 0 to pi of (4 sin theta -3 cos theta) d theta
    I started like this...4 integral from 0 to pi of sin theta d theta -3 integral from 0 to pi cos theta d theta...I got stuck here


    what do you mean you "got stuck"? do you know the antiderivatives of sine and cosine ? do you know how to use the fundamental theorem of calculus?


    2. How do I calculate this math?
    3/4 (8^4/3) - 3/4 (1^4/3) =?


    8^{\frac{4}{3}} = \left(8^{\frac{1}{3}}\right)^4 = 2^4 = 16

    1 to any power is 1.


    3. How do I solve this integral?
    integral of cos^3 x dx


    cos^3{x} = cos^2{x} \cos{x} = (1 - \sin^2{x})\cos{x} = \cos{x} - \sin^2{x}\cos{x}

    \int \cos{x} \, dx - \int \sin^2{x}\cos{x} \, dx

    straight up integration of the first integral ... use substitution for the second , let u = \sin{x}
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